SM4.2 Ratio, proportion and rates
You can split quantities in a given ratio, scale recipes and mixtures, and solve speed, time and distance and work-rate questions by reasoning about rates.
Topics shown in module order.
A ratio compares parts to parts, a rate compares different kinds of quantity, and proportion is the statement that two of them are equal. Almost every arithmetic question an examination asks after school is one of these three in costume: sharing an amount, mixing at a ratio, a train covering distance, two people painting a wall together. The unifying habit is finding the value of one part or one unit of time, and building the answer from it.
Work through these
Divide quantities in a given ratio by finding the value of one part first
One part is the atom of every ratio question, and finding it first works unchanged when the ratio has three terms or the total is a difference instead of a sum. It is the unitary method earning its keep.
Solve direct and inverse proportion questions, saying which kind each is before computing
More workers mean fewer days but more cloth means more money, and mixing the two directions is the standard error. Classifying before calculating makes the direction a decision rather than an accident.
Solve speed, time and distance questions, including one average-speed trap over a round trip
Average speed over a round trip is not the average of the two speeds, because the slower leg takes longer. The round-trip question is asked in some form nearly everywhere, and understanding the why immunises better than the shortcut formula.
Solve work-rate questions by converting each worker to work done per unit of time
If one pipe fills a tank in six hours it fills a sixth per hour, and rates per hour add even though times do not. That single conversion dissolves the entire together-and-alone family of questions.
Practice you have recorded
Optional, and yours. This records that you say you worked on this topic. It is not a check of whether you got anything right.
Sign in free to record your practice and keep it if you change phones.
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 7 Sept 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…